MMN-1670

# On strongly prime submodules

*Abdulrasool Azizi*;

## Abstract

Let $R$ be a commutative ring with identity and $M$ an $R$-module. A proper submodule $N$ of $M$ is called strongly prime [resp. strongly semiprime], if $((N+Rx):M)y\subseteq N$ [resp. $((N+Rx):M)x\subseteq N$] for $x,y\in M$ implies that $x\in N$ or $y\in N$ [resp. $x\in N$]. Strongly prime and strongly semiprime submodules are studied, in this paper.

Vol. 19 (2018), No. 1, pp. 125-139

DOI: 10.18514/MMN.2018.1670